Even though your landlord carries insurance on the building itself, you still need coverage for your personal assets when renting. Renter's insurance would cover your personal property and provide you with liability coverage.
Renter's insurance would ensure you have coverage of your personal property in the event of a fire, natural disaster, etc. Examples of items that are considered personal property include furniture, jewelry, smart phone, computer equipment, television, clothing, and collectibles.
You may only pay rent, but you could be held liable for injuries sustained within your rental. Events such as dog bites, slips and falls, and even inappropriate behavior of a family member or guest could fall under your responsibility. Renter's insurance will provide liability coverage to protect you from instances like these.